12n
0223
(K12n
0223
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 12 9 4 6 8 5 6 11
Solving Sequence
4,7 6,8
9
3,12
5 2 1 11 10
c
7
c
8
c
3
c
5
c
2
c
1
c
11
c
10
c
4
, c
6
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.05608 × 10
32
u
27
+ 2.39983 × 10
32
u
26
+ ··· + 4.71199 × 10
33
d − 1.14579 × 10
30
,
− 7.16121 × 10
28
u
27
+ 2.11432 × 10
32
u
26
+ ··· + 9.42397 × 10
33
c + 9.50662 × 10
33
,
7.43837 × 10
31
u
27
− 2.05180 × 10
32
u
26
+ ··· + 4.71199 × 10
33
b − 3.81499 × 10
32
,
5.68907 × 10
31
u
27
− 1.81131 × 10
32
u
26
+ ··· + 1.88479 × 10
34
a − 1.63326 × 10
34
, u
28
− 3u
27
+ ··· − 64u + 32i
I
u
2
= h−7778149750u
19
a + 21085480149u
19
+ ··· + 37111822100a − 70739740318,
18555911050u
19
a − 33847094283u
19
+ ··· − 266919956828a + 210342367834,
4182326921u
19
a + 3076005459u
19
+ ··· − 29433713862a + 28068851486,
49133842327u
19
a − 33157787379u
19
+ ··· − 204672432210a + 75288972938,
u
20
+ u
19
+ ··· − 8u − 4i
I
v
1
= hc, d − v, b, a − 1, v
2
+ v + 1i
I
v
2
= ha, d + v, −av + c − v − 1, b + 1, v
2
+ v + 1i
I
v
3
= ha, d − 1, c + a, b + 1, v + 1i
I
v
4
= ha, d
2
a + d
2
v + dc − dv − d + v + 1, d
2
v
2
− v
2
d − dv + v
2
+ 2v + 1,
dca + dcv − da − dv + c
2
− cv − av − 2c − a + 1, v
2
dc − v
2
d − v
2
c − v
2
a − cv − 2av − a,
dav + da + dv + cv + c − v − 1, c
2
v
2
+ v
2
ca + a
2
v
2
+ cav − v
2
c + 2a
2
v + v
2
a + a
2
+ av + v
2
, b + 1i
* 5 irreducible components of dim
C
= 0, with total 73 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
1